DI RECTIVE WORDS OF EPISTURMIAN WORDS:EQUI VALENCES AND NORMALIZATION

Ep isturmian morphisms con stitute a p owerful to ol to studyep isturmian words. I ndeed , any ep isturmian word can b e infinitely de-comp osed over the set of pure episturmian morphisms. Thus, an epis-t u rm ian word c an b e d e fi n e d by on e of it s m orp h ic d ecom p osit ion s or,eq u ivalent ly, by a certain d irective word . H ere we ch aracterize p airsof words d irecting the same episturmian word. We also p rop ose a wayto uniquely d efine any episturmian word through a normalization ofits d irective word s. A s a c on seq u en ce of th ese r esu lts, we ch aracterizeep isturmian words having a unique d irective word